This paper describes the problem of online autonomous mobile robot path planning, which is consisted of finding optimal paths or trajectories for an autonomous mobile robot from a starting point to a destination across a flat map of a terrain, represented by a 2-D workspace. An enhanced algorithm for solving the problem of path planning using Bacterial Foraging Optimization algorithm is presented. This nature-inspired metaheuristic algorithm, which imitates the foraging behavior of E-coli bacteria, was used to find the optimal path from a starting point to a target point. The proposed algorithm was demonstrated by simulations in both static and dynamic different environments. A comparative study was evaluated between the developed algori

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

In this study, the photodegradation of Congo red dye (CR) in aqueous solution was investigated using Au-Pd/TiO₂ as photocatalyst. The concentration of dye, dosage of photocatalyst, amount of H₂O₂, pH of the medium and temperature were examined to find the optimum values of these parameters. It has been found that 28 ppm was the best dye concentration. The optimum amount of photocatalyst was 0.09 g/75 mL of dye solution when the degradation percent was ~ 96 % after irradiation time of 12 hours, while the best amount of hydrogen peroxide was 7μl/75 mL of dye solution at degradation percent ~97 % after irradiation time of 10 hours, whereas pH 5 was the best value to carry out the reaction at the highest deg

In this study, the photodegradation of Congo red dye (CR) in aqueous solution was investigated using Au-Pd/TiO2 as photocatalyst. The concentration of dye, dosage of photocatalyst, amount of H2O2, pH of the medium and temperature were examined to find the optimum values of these parameters. It has been found that 28 ppm was the best dye concentration. The optimum amount of photocatalyst was 0.09 g/75 mL of dye solution when the degradation percent was ~ 96 % after irradiation time of 12 hours, while the best amount of hydrogen peroxide was 7μl/75 mL of dye solution at degradation percent ~97 % after irradiation time of 10 hours, whereas pH 5 was the best value to carry out the reaction at the highest degradation percent. In additio

In this study, the photodegradation of Congo red dye (CR) in aqueous solution was investigated using Au-Pd/TiO2 as photocatalyst. The concentration of dye, dosage of photocatalyst, amount of H2O2, pH of the medium and temperature were examined to find the optimum values of these parameters. It has been found that 28 ppm was the best dye concentration. The optimum amount of photocatalyst was 0.09 g/75 mL of dye solution when the degradation percent was ~ 96 % after irradiation time of 12 hours, while the best amount of hydrogen peroxide was 7μl/75 mL of dye solution at degradation percent ~97 % after irradiation time of 10 hours, whereas pH 5 was the best value to carry out the reaction at the highest degradation percent. In additio

The aim of the research is to present and discuss the subject of the budgeting estimates and how to activate the role of the Federal board of supreme audit in examining these estimates through reference to Articles 6 and 10 of the Federal board of supreme Law, which did not restrict Federal board of supreme in Preventive control on examination process for planning which is prepared from the government units, as the result of a large amount  of government units Provisions and the weakness of estimates in most of its items, which rely on personal assessment and not based on scientific and logical basis of the estimate, which leads to the emergence of a deficit is not true in the general budget and this seems clear in most Iraq

Current search problem manifested and widows who community harsh to bear hardships and pains، The goals of continuing the sustainability of life and take responsibility, and especially in light of the difficult circumstances in which Iraq is going through, and the displacement of murder and terrorism, which generated huge numbers of widows and orphans Because of the loss of a breadwinner and which became women and children are the most harm to the victim and as a result of wars and armed tendencies So this research is an important and vital topic opens our horizons important for overlapping roles of women widows and their impact on the achievement and status of Iraqi women and that as long as aptly characterized and their ability to end

The purpose of this research is to determine the extent to which independent auditors can audit the requirements of e-commerce related to (infrastructure requirements, legislation and regulations, tax laws, and finally human cadres). To achieve this, a questionnaire was designed for auditors. Numerous statistical methods, namely arithmetic mean and standard deviation, have been used through the implementation of the Statistical Packages for Social Sciences (SPSS) program.

The research has reached several results, the most important of which are: There are noobstacles to enabling the auditor to audit the application of the e-commerce requirements as well as the respective(infrastructure requirements, legislation and regulations, t